Berkeley's Analyst: Rigour and Rhetoric - Moriarty, Clare (King's College London, 2018)
Consider the following puzzle: in 1732, Berkeley published Alciphron, and with it a sweeping pragmatic vindication of concepts whose terms fail to represent clear ideas. In that pragmatic semantics, he uses mathematical terms as a model example, maintaining that they represent a case where searching for ideas represented, instead of focusing on the functional and instrumental role played, is mistaken and ‘sure to embarrass’ (Alciphron, D7 §18) those who take this analytical approach. ‘Infinitesimals’ are among the examples he chooses as relevant examples for this treatment, which should surprise those familiar with his earlier philosophy. Moreover, it is clear that he sees this understanding of meaning as vital to rescuing certain religious and scientific concepts from accusations of obscurity. Just two years later, Berkeley publishes The Analyst, containing a thoroughgoing and scathing attack on calculus, despite its acknowledged utility and fruitfulness. Further, the criticism focuses on the incoherence of infinitesimals, and often on the very grounds he rejected as illegitimate critical in exactly such cases two years earlier. Moreover, in The Analyst, Berkeley seems to have a newfound appreciation for the general laudableness of mathematics in a way that, again, should strike those familiar with his earlier work as peculiar. There are various interpretive options to address the puzzle: perhaps, Berkeley was just inconsistent, and in his desire to criticise certain calculus enthusiasts, didn’t worry about the clash it posed with his earlier theory of meaning; or, perhaps he just changed his mind, and saw that the pragmatic account was inconsistent with criticisms he thought important, and more, he really had come to respect the foundations of classical mathematics; or, perhaps he moved from a general account of semantics to a mixed one where utility can rescue meaningfulness in certain restricted kinds of language use, but not in others. In this thesis, I offer my preferred solution. It is one that requires detailed attention to a number of features of Berkeley’s philosophy and context. This dissertation offers a novel interpretation of The Analyst based on Berkeley’s mature theory of meaning and its role in his views on religion and 14 mathematics. I argue that we should read the main text of The Analyst as consisting in an argumentum ad hominem3 against ‘freethinkers’ who alleged that a mathematical/logicist criterion of intelligibility showed significant parts of religion to be unintelligible and irrational.4 By showing that the same standards (standards inspired by mathematics and logic) demonstrate the irrationality of calculus, he provides a reductio argument against this freethinking methodology. The text has typically been read as constituting a significant change in Berkeley’s position on the philosophy of mathematics—one involving a newly conciliatory outlook on the foundations and axioms of classical mathematics and an abandonment of the sweeping semantic pragmatism advanced by Euphranor at the end of Alciphron.5 I argue that this ostensible endorsement of the foundations of traditional mathematics is merely a necessary condition of an internal argument Berkeley wishes to use to demonstrate that the calculus fails its own discipline’s tests of rigour. Further, by reading the text as I suggest, we can reconcile the arguments of The Analyst with the pragmatic theory of word meaning endorsed in the decisive argument of the final dialogue of Alciphron. The Analyst is a complex work, the understanding of which requires the integration of three strands of Berkeleyan philosophy. At the forefront of his 1730s philosophy is a deep, almost neurotic concern with the future of Anglican morality and the future of western European society. This anxiety is visible in Alciphron and The Analyst, but perhaps even more pronounced in his social and homiletic writings in the surrounding period—SIS, MIM and WTW—and his personal correspondences.
PUBLISHED
Keywords: CALCULUS; George Berkeley; Philosophy of Mathematics